Problem 60 - Chemistry The Central Science In Si Units

Question

Under constant-volume conditions, the heat of combustion of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) is \(40.18 \mathrm{~kJ} / \mathrm{g}\). A \(2.50-\mathrm{g}\) sample of naphthalene is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.50 to \(28.83^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) A 1.50-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 21.14 to \(25.08^{\circ} \mathrm{C}\). What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

Step-by-Step Solution

Answer

(a) 13.70 kJ/°C; (b) 35.96 kJ/g; (c) The heat capacity decreases.

Step 1: Calculate the Total Heat Released by Naphthalene

The heat released by the naphthalene is calculated using its heat of combustion.Given: - Heat of combustion of naphthalene = 40.18 kJ/g- Mass of naphthalene = 2.50 gThe total heat released (q) is:\[ q = \text{heat of combustion} \times \text{mass} = 40.18 \, \frac{\text{kJ}}{\text{g}} \times 2.50 \, \text{g} = 100.45 \, \text{kJ} \]

Step 2: Calculate the Total Heat Capacity of the Calorimeter

The total heat capacity (atured capital "C") of the calorimeter is the amount of heat required to raise its temperature by one degree Celsius.The given temperature change (ΔT) is 7.33°C (from 21.50°C to 28.83°C).Use the formula:\[ q = C \times \Delta T \]so,\[ C = \frac{q}{\Delta T} = \frac{100.45 \, \text{kJ}}{7.33 \, ^{\circ}\text{C}} = 13.70 \, \text{kJ}/^{\circ}\text{C} \]

Step 3: Calculate Heat Released by New Substance

For the new organic substance:Given:- Mass of the new substance = 1.50 g- Temperature change = 3.94°C (from 21.14°C to 25.08°C)Using the heat capacity of the calorimeter (Step 2), calculate the heat released:\[ q = C \times \Delta T = 13.70 \, \text{kJ}/^{\circ}\text{C} \times 3.94 \, ^{\circ}\text{C} = 53.94 \, \text{kJ} \]

Step 4: Calculate Heat of Combustion per Gram of New Substance

The heat of combustion per gram of the new substance is calculated by dividing the total heat released by the mass.\[ \text{Heat of combustion per gram} = \frac{53.94 \, \text{kJ}}{1.50 \, \text{g}} = 35.96 \, \text{kJ}/\text{g} \]

Step 5: Discuss Effect of Water Loss on Calorimeter Heat Capacity

Losing water from the calorimeter decreases its total heat capacity. With less water, the calorimeter would require less heat to achieve the same temperature change, effectively lowering its heat capacity.

Key Concepts

Heat of Combustion

The heat of combustion is an important concept in calorimetry. It refers to the amount of heat energy released when a substance undergoes complete combustion in the presence of oxygen. This energy is usually measured in kilojoules per gram (kJ/g). When a fuel like naphthalene is burned, it reacts with oxygen to form water and carbon dioxide, releasing a significant amount of energy.

The magnitude of the heat of combustion gives us insight into the energy content of the substance. Substances with a high heat of combustion, like naphthalene with 40.18 kJ/g, are potent energy sources. This value is crucial in calculations involving fuel efficiency and heat production.

Bomb Calorimeter

A bomb calorimeter is an essential laboratory device used to measure the heat of combustion of a substance. It consists of a sturdy, sealed container known as a "bomb," which holds the sample and oxygen for combustion. The bomb is submerged in water to absorb the heat released during the reaction.

This equipment measures the temperature change of the water, which helps determine the total heat energy released. Because bomb calorimeters operate at constant volume, they are particularly good at measuring the energy in reactions like combustion. These devices are vital for obtaining accurate and reliable data on the heat output of various organic and inorganic substances.

Heat Capacity

Heat capacity is an intrinsic property of the calorimeter and any substance involved in the experiment. It is defined as the amount of heat needed to increase the temperature of the entire system by one degree Celsius. In this context, we used the relationship between heat capacity, heat released, and temperature change: \[ q = C \times \Delta T \]Where \( q \) is the heat absorbed or released, \( C \) is the heat capacity, and \( \Delta T \) is the temperature change.

In a bomb calorimeter, the heat capacity includes the contribution from both the calorimeter itself and any other contents, like water. Knowledge of the calorimeter's heat capacity allows us to accurately calculate the energy change from the temperature change observed during an experiment.

Organic Substances Combustion

Combustion of organic substances involves the reaction of these compounds with oxygen, producing carbon dioxide and water with the release of heat. This process is fundamental in energy production and is extensively studied in the context of fuels.

Organic compounds, typically containing carbon, hydrogen, and sometimes oxygen, release energy when their chemical bonds break and form new bonds during combustion. Understanding these reactions helps in evaluating the efficiency and environmental impact of fuels.

• Natural and synthetic organic substances can vary widely in their heat of combustion.
• Accurate measurements of this heat are vital for applications ranging from engine design to environmental monitoring.

Knowledge of combustion processes is essential for the development and optimization of fuel usage.